Construction of Periodic Prolate Spheroidal Wavelets Using Interpolation
Xiaoping Shen, Gilbert G. Walter · Numerical Functional Analysis and Optimization · 2007
Periodic prolate spheroidal wavelets (periodic PS wavelets), based on the periodizaton of the first prolate spheroidal wave function (PSWF), were recently introduced by the authors. Because of localization and other properties, these periodic PS wavelets could serve as an alternative to Fourier series for applications in modeling periodic signals. In this paper, we continue our work with periodic PS wavelets and direct our attention to their construction via interpolation. We show that they have a representation in terms of interpolation with the modified Dirichlet kernel. We then derive a group of formulas of interpolation type based on this representation. These formulas enable one to obtain a simple procedure for the calculation of the periodic PS wavelets and finding expansion coefficients. In particular, they are used to compute filter coefficients for the periodic PS wavelets. This is done for a number of concrete cases.